Recall that the nilpotent radical \(\mathfrak {n}\)  of a Lie algebra \(\mathfrak {g}\)  is the intersection of the kernels of all irreducible representations of \(\mathfrak {g}\)  ([1]} or [2]}). Similarly, the nilpotent radical \(N\)  of a complex Lie group \(G\)  is the intersection of the kernels of all irreducible holomorphic representations of \(G\) . We follow the terminology in [2]}, [4]}; in [5]} the term `representation radical' is used. It is obvious that \(N\)  is a closed normal subgroup of \(G\) .
